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CBSE Class 8  >  Class 8 Test  >  Mathematical Olympiad   >  Olympiad Test: Algebraic Expressions And Their Identities - 1 - Class 8 MCQ

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Free MCQ


MCQ Practice Test & Solutions: Olympiad Test: Algebraic Expressions And Their Identities - 1 (20 Questions)

You can prepare effectively for Class 8 Mathematical Olympiad Class 8 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Olympiad Test: Algebraic Expressions And Their Identities - 1". These 20 questions have been designed by the experts with the latest curriculum of Class 8 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 40 minutes
  • - Number of Questions: 20

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Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 1
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What are the factors of the expression ab – a - b + 1?

Detailed Solution: Question 1

- To factor the expression ab - a - b + 1, start by grouping terms.
- Rewrite it as ab - a - b + 1 = a(b - 1) - 1(b - 1).
- Notice that both terms contain (b - 1).
- Factor out (b - 1): (b - 1)(a - 1).
- This shows that the expression can be represented as the product of (a - 1) and (b - 1).
- Therefore, the correct answer is (a - 1)(b - 1).

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 2
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If (2x - 3) is a factor of 6x2 – 7x – 3, then what is the other factor?

Detailed Solution: Question 2

6x2 – 7x – 3

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Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 3
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What are the factors of (g + h)2 - 4gh ?

Detailed Solution: Question 3

To Simplify the expression: (g+h)2 − 4gh

Step1: Expand
(g+h)2 = g2 + 2gh + h2

Step2: Substitute and simplify
g2 + 2gh + h2 − 4gh = g2 − 2gh + h2

Step3: Factor
g2 − 2gh + h2 = (g−h)(g−h)

So, Correct Option:B

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 4
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If one of the factor of 25(x + y)2 – 36 (x – 2y)2 is (17y – x), then what is the other factor?

Detailed Solution: Question 4

25 (x + y)2 – 36 (x – 2y)2

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 5
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Find the value of (a + 1) (a – 1) (a2 + 1).

Detailed Solution: Question 5

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 6
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If x + y = 12 and xy = 14 then what is the value of x2 + y2?

Detailed Solution: Question 6

(x + y)2 = x2 + y2 + 2xy

                = 116

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 7
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​If  then what is the value of 

Detailed Solution: Question 7

 = 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 8
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If x + y = 10 and xy = 9, what is the value of x2 – y2?

Detailed Solution: Question 8

( x + y) 2 = x2 + y2+ 2xy


∴ 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 9
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If   then find the value of .

Detailed Solution: Question 9



Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 10
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The perimeter of a triangle is 6m2 – 4m + 9 and two of the sides are m2 – 2m + 1 and 2m2 + 3m + 5. What is the third side?

Detailed Solution: Question 10

Third side = 6m2 – 4m + 9 – (m2 – 2m + 1 + 2m2 + 3m + 5)

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 11
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What is the remainder when 7 + 15x – 13x2 + 5x3 is divided by 4 – 3x + x2?

Detailed Solution: Question 11


Clearly (x - 1) is remainder.

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 12
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What is the quotient if x4 – 2x3 + 2x2 + x + 4 is divided by x2 + x + 1?

Detailed Solution: Question 12


∴ Quotient = x2 - 3x + 4

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 13
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What is the quotient if 5x3 – 4x2 + 3x + 18 is divided by 3 – 2x + x2?

Detailed Solution: Question 13

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 14
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​If  then what is the value of 

Detailed Solution: Question 14


Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 15
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 8a2 b3 ÷ (-2ab)?

Detailed Solution: Question 15

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 16
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What is the value of 

Detailed Solution: Question 16

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 17
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What is the numerical coefficient in the product of 2abc, - 16a2bc and 3ab2c2?

Detailed Solution: Question 17

The product of the expressions can be calculated as follows:

  • Start with the three expressions: 2abc, -16a2bc, and 3ab2c2.
  • Multiply the coefficients: 2 × -16 × 3.
  • Calculating step-by-step:
    • First, 2 × -16 = -32.
    • Next, -32 × 3 = -96.
  • Now, combine the variables:
    • abc × a2bc × ab2c2 = a4b4c3.

Thus, the final result is:

-96a4b4c3.

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 18
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​If  what is the value of ?

Detailed Solution: Question 18


Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 19
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What is the value of 

Detailed Solution: Question 19


 

Olympiad Test: Algebraic Expressions And Their Identities - 1 - Question 20
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What is the remainder when 6x2 – 11x + 15 is divided by 2x – 5?

Detailed Solution: Question 20

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About this Class 8 Practice Test

This test contains 20 MCQs on Olympiad Test: Algebraic Expressions And Their Identities - 1 with detailed solutions for each question. It is part of the Mathematical Olympiad Class 8 course on EduRev, designed to align with the current Class 8 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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If you found this Olympiad Test: Algebraic Expressions And Their Identities - 1 MCQ Test helpful, you can further enhance your Class 8 preparation with in-depth courses on EduRev, for all the subjects and topics available in Mathematical Olympiad Class 8 course. The course offers:
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